Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #67579 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#67582 |
| Sylow | C3 ⋊ C2×#1426 |
190 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10715812, C2×D3×#1426, C2×#10715815 |
| maximal normal subgroup of | C2×#10715812, C2×D3×#1426, C2×#10715815 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 90086);